42. y tanx)/3x2+5x3 + sin x4243-50 Find an equation for the tangent line to the graph at thespecified value of x.43. y= xcos 3x, x7T44. y sin (1 +x), x= -345. y sec x), x==2--)346. y=247. y tan (4x), x = VTX48. y 3 cot x, x4249. y x5- x2, x= 1X50. y 1-2t 051-54 Find dy/dx252. y sin (3x-)51. y xcos (5x) sin xX(G)154. y xtan1 +x53. y 1 Xx55-58 Find the indicated derivative.dy55. y cot (T- 0); finddo6au +b(a, b, c, d constants).du; find56. A=си + d2(a, b constants)[a cos Tw+b sin Tw]57.dwdx- ese -):y; finddy2= CSC358. xf the func-

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Asked Sep 19, 2019
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#43

42. y tan
x)/3x2+5
x3 + sin x
4
2
43-50 Find an equation for the tangent line to the graph at the
specified value of x.
43. y= xcos 3x, x
7T
44. y sin (1 +x), x= -3
45. y sec x), x
==
2
--)
3
46. y
=2
47. y tan (4x), x = VT
X
48. y 3 cot x, x
4
2
49. y x5- x2, x= 1
X
50. y 1-2t 0
51-54 Find dy/dx2
52. y sin (3x-)
51. y xcos (5x) sin x
X
(G)
1
54. y xtan
1 +x
53. y 1 X
x
55-58 Find the indicated derivative.
dy
55. y cot (T- 0); find
do
6
au +b
(a, b, c, d constants).
du
; find
56. A=
си + d
2
(a, b constants)
[a cos Tw+b sin Tw]
57.
dw
dx
- ese -):
y; find
dy
2
= CSC
3
58. x
f the func-
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42. y tan x)/3x2+5 x3 + sin x 4 2 43-50 Find an equation for the tangent line to the graph at the specified value of x. 43. y= xcos 3x, x 7T 44. y sin (1 +x), x= -3 45. y sec x), x == 2 --) 3 46. y =2 47. y tan (4x), x = VT X 48. y 3 cot x, x 4 2 49. y x5- x2, x= 1 X 50. y 1-2t 0 51-54 Find dy/dx2 52. y sin (3x-) 51. y xcos (5x) sin x X (G) 1 54. y xtan 1 +x 53. y 1 X x 55-58 Find the indicated derivative. dy 55. y cot (T- 0); find do 6 au +b (a, b, c, d constants). du ; find 56. A= си + d 2 (a, b constants) [a cos Tw+b sin Tw] 57. dw dx - ese -): y; find dy 2 = CSC 3 58. x f the func-

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Expert Answer

Step 1
The given function is f(x) xcos3x.
Find the slope of the tangent on the curve as follows
dy
(xcos3x)
dx dx
-(c03) )=f-g+fe|
d
d
= cos3x
dx
g +
dx
=1 cos3.x 3sin 3x).x
=cos3.x -3xsin 3.x
Substitute the value ofx = n in the slope of the tangent
aycos3x 3xsin 3x
dx
— cos3л - 3лsin 3л
= -1
help_outline

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The given function is f(x) xcos3x. Find the slope of the tangent on the curve as follows dy (xcos3x) dx dx -(c03) )=f-g+fe| d d = cos3x dx g + dx =1 cos3.x 3sin 3x).x =cos3.x -3xsin 3.x Substitute the value ofx = n in the slope of the tangent aycos3x 3xsin 3x dx — cos3л - 3лsin 3л = -1

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